SOLUTION: I need to find the total surface area of a stand that was cut from a right circular cone (now called a frustum of a cone). The height is 40 cm,bottom radius is 100 cm, and the t

Algebra ->  Surface-area -> SOLUTION: I need to find the total surface area of a stand that was cut from a right circular cone (now called a frustum of a cone). The height is 40 cm,bottom radius is 100 cm, and the t      Log On


   

Question 40018: I need to find the total surface area of a stand that was cut from a right circular cone (now called a frustum of a cone).
The height is 40 cm,bottom radius is 100 cm, and the top radius is 60 cm.
Answer by venugopalramana(3286) About Me  (Show Source):
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I need to find the total surface area of a stand that was cut from a right circular cone (now called a frustum of a cone).
The height is 40 cm,bottom radius is 100 cm, and the top radius is 60 cm.
let the original cone have AB as its altitude with A as vertex and B as the centre of the base.let C be a point on perimeter at the bottom.so AC is the slant height.
let D be the point on the axis at the top of the frustrum and E is point on slant height AC..we have
AB=H say
BC=radius at bottom = 100
DE radius at top=60
BD=frustum ht=40
AD=AB-BD=H-40
triangles ABC,ADE are similar.hence
AB/AD=BC/DE
H/(H-40)=100/60=5/3
3H=5H-200
2H=200
H=100
AD=100-40=60
so
volume of frustum= volume of full cone-volume of cut cone = (3.14/3){100*100*100-60*60*60}=820587